To solve the equation

[
\frac{2x-18}{x^{2} -13x+36} = 0
]

we first need to find the values of (x) that make the numerator of the fraction equal to 0:

[
2x - 18 = 0
]

[
2x = 18
]

[
x = 9
]

Now we have found that the numerator is equal to 0 when (x = 9). Next, we need to find the values of (x) that make the denominator equal to 0:

[
x^{2} - 13x + 36 = 0
]

We can factor the quadratic equation to get:

[
(x - 9)(x - 4) = 0
]

Setting each factor equal to 0:

[
x - 9 = 0 \quad \text{or} \quad x - 4 = 0
]

[
x = 9 \quad \text{or} \quad x = 4
]

So the values of (x) that make the denominator of the fraction equal to 0 are (x = 9) and (x = 4).

However, since the original equation is a fraction, the value of the fraction will only be 0 when the numerator is 0 but the denominator is not 0. Therefore, the only solution to the equation is (x = 4).